Relative Probability Synchronization for Dynamical Systems Created by Homeomorphisms

In this paper, using the relative probability measure, the notion of synchronized dynamical systems from the viewpoint of an observer for discrete topological dynamical systems created by the homeomorphisms of a metric space, is considered. A kind of equivalence relation up to the suitable observers, is deduced. It is proved that: topological conjugacy implies to the relative probability synchronization. The notion of relative probability synchronization for the ideal observers on the probability spaces, is studied. The relative probability synchronization of the time one maps of the solutions of Chuaʹs diode and its driven system by the different observers, are studied.